Appendix A. Statistical Models

This appendix describes the statistical models used in this study. These include
the multivariate logit analyses used in Phase I and the multivariate hazard
analyses used in Phase II.

We adopted a 95 percent confidence level for rejecting the null hypothesis
throughout this report. A 95 percent confidence level means that there is
a 5 percent chance of incorrectly rejecting the null hypothesis and concluding
that the differences observed in the sample are significant.

We followed the statistical convention of testing the null hypothesis. In
this case, the null hypothesis states that, after controlling for other
factors, the probability that an outcome occurs for female doctorate recipients
is
not
different from the probability that the same outcome will be observed for
male doctorate recipients. Rejecting the null hypothesis allows us to accept
the
alternative hypothesis that the probabilities are different. If we can
accept the alternative hypothesis, we might infer an association between sex
and
the outcome (i.e., employment in a tenure-track position, earning tenure,
or employment
in different academic ranks).

Logit Analysis

The logit analyses allow us to determine whether sex is related to the likelihood
that a given outcome will occur after accounting for the contributions of other
controlling variables. We do this by comparing the likelihood that a given
outcome will occur for female doctorates with the likelihood that the outcome
will occur for male doctorate recipients, holding constant other factors that
might be related to outcomes.

The Phase I estimates presented in Sections 3 and 4 of this report are the
marginal relations between the female variables and the likelihood of an outcome
occurring and are not the estimates of the α and β. These marginal relations,
typically referred to as "marginal effects," are given by the partial
derivative of the probability of the outcome occurring with respect to the
female variables. For example, the marginal effect of the kth female variable
is given by

computed at the sample means of X and F. We computed the marginal effects
of the controlling variables analogously.[1] We provide complete estimates of
the logit models in Appendix C. Note that the estimates reported there are
the marginal effects and are not estimates of the α and β. We provide an alphabetical
list of variable acronyms in Appendix B.

Note that the logit models for the tenure track and tenure analyses are binomial
in that only two outcomes are possible (e.g., the individual is either tenured
or not tenured). However, the logit models for the academic rank analyses
are multinomial in that several (three) outcomes are possible (i.e., junior
ranks,
associate professor rank, or full professor rank).

We generally included cases when observations were missing for independent
variables and included missing dummy variables as controls. However, we
excluded cases in which information required to define the dependent variable,
(i.e.,
career outcomes) was missing.[2]

Hazard Analysis

Hazard analysis allows us to estimate the likelihood that an outcome will
be observed for an individual at any given time, conditional on the fact that
the outcome has not occurred previously for that individual. We employed the
Cox proportional hazard model in our Phase II analyses. The structure of the
model is

where

t = time (years since doctorate);
h(t,F,X) = the hazard rate at time t, conditional on F and X;
h(t,0,0) = the baseline hazard rate; and
all else is as previously defined.

The probability of an outcome occurring for an individual at time T* can be written

where Rk is the set of indivicuals with durations greater than or equal to T*, and all else is as previously defined.

In Sections 3 and 4 of this
report, we present Phase II estimates of the marginal relations between
the female variables and the likelihood of outcomes occurring. These marginal relations,
typically referred to as "relative risks" (e.g., the risk of moving
from the untenured state to being tenured), give the ratio of the probability
of an outcome for a surviving (e.g., untenured) female doctorate recipient
to the probability for a similarly situated male doctorate recipient. For example,
for the FEMALE[3] variable,
the relative risk is given by

Although we report relative risks in the tables presented in Sections
3 and
4 of this report, the tables in Appendix D report the estimated coefficients
of the hazard function (i.e., the α and β). These can be converted to estimates
of relative risks by exponentiation of the estimated coefficients.

Footnotes

[1] The
logit models were estimated using LIMDEP ver. 7.0. See Greene,
1995.

[2] We
followed this convention in all the multivariate analyses conducted for this
study.